Download Patty Paper Geometry

Patty Paper Geometry
The mid-segments of a
triangle
Step 1: Draw or Fold a large acute scalene triangle on your patty
paper. Then label each of the angles  A ,  B, and  C.
B
A
Step 2: Fold the sides of the triangle onto each other and “pinch”
the paper to construct the midpoints of the three sides of
the triangle.
“pinch”
C
B
Step 3: Draw a line segment connecting the mid points. Repeat
this for each of the 3 mid points. It should make 4
smaller triangles inside the original larger one.
A
C
Step 4: Use a second piece of patty paper to trace one of the
four smaller triangles. Then compare all four of the
smaller triangles. Compare the results with your group.
Write a Conjecture:
Complete the sentence with a conjecture about the three mid segments of a triangle:
The three midsegments of a triangle divide it into _____________________________ .
Step 5: Use an edge of the 2nd piece of patty paper to compare
the length of the mid-segment with the length of the
base that is called the corresponding base. This is the
side of the triangle that does not contain either end of
the mid-segment. (In the sketch to the right it is side BC is the
corresponding base to the mid-segment shown)
B
Step 7: Fold angle B down along the mid-segment hk, then fold
 A to  B and  C to  B as well. This should form a
quadrilateral.
Points to Ponder !
o What type of Quadrilateral does it form?
o What do you know about the sides of this quadrilateral ?
o How does mid-segment hk compare with the
corresponding side AC ?
PP Midsegments
1
C
A
Step 6: Draw the other two mid-segments, and compare their
lengths with their corresponding bases. (side AC is the
corresponding base to the midsegment hk )
h
A
k
B
A
B
C
C
revised: 10/22/2013
Patty Paper Geometry
Write a Conjecture:
Complete the sentence with a conjecture about the midsegment of a triangle:
The length of the midsegment of a triangle is _____________________________________
__________________________________________________________________________
PART 2
Step 9: With all of the midsegments drawn and the triangle
unfolded, number each of the angles formed. Then use
a second piece of patty paper to copy  A .
Step 10: Slide this second piece of patty paper so that you move
the angle  A that you traced. Place it so that it is now
located over  6 and compare the angles. Repeat this
and compare  B and  1.
B
2
1 3
A
8
5
24 6
7
C
Points to Ponder !
 What do you remember about the corresponding angles postulate and its converse?
 Based upon this postulate and the investigations you have done with these midsegments,
what conclusions can you make about the midsegment and the triangles larger side?
If these angles ( A and  6) are congruent, and ( B and  1) are congruent, and ( C
and  8) are congruent, then we can say that the lines are parallel. Compare results
with the others at your table to see if they have similar findings. Then write your final
two conjectures.
Write a Conjecture:
Complete the sentence with a conjecture about the midsegment of a triangle:
The midsegment of a triangle is _____________________ to its corresponding base.
IN Summary, all the Conjectures say:
The midsegment of a triangle of a triangle divides it into ______________________ ,
is _____________________ to its corresponding base, and with
a length that is _____________ the size of that base.
PP Midsegments
2
revised: 10/22/2013